(20) 



7 he Indices of Doubly- refracting Crystals. 827 



A solution of these equations yields, if e _1 = l — a) 2 (x 2 + y 2 )/C 2 , 

 e- 1 a = aXl-coy/C 2 ) + ±™3eh f + to 2 xyV j(¥ ^ 

 e" 1 & = &' (1 - a>VyC 2 ) + ±7rayyh' + ©%a'/C 9 

 e" 1 c = 6 y - 47ra>(.r/'' + ?/#') 



e -i/=// (l~afy/(?)-*wxJ/4!ir& + <D 2 xyg f \Q 2 j 

 €- l c, = g'(l -coV/C 2 ) - a)2/c747r0 2 + o>%/7C 2 | 

 e- 1 /iW/-r^a'# + %)/47rC 2 . J 



On substitution in (16) the circuital relations take the form, 

 quoting only the first, 



Take now a new time variable t' f such that 



dt'' = dt , -we{xdy-ydx)IO\ . . . (21) 



which may be recognized at once as identical with the time 

 chosen in the other method, for xdy—ydx = r 2 d0. Then if 



6i -i=l- w V/C 2 , e- l = l-coy/G 2 , . . (22) 

 we obtain 



~d /€ P , co 2 e xyq'\ e , a> 2 wy 2 ef' .A , , , 7 , , N 



WW ~W' 7/ + ~& ' eh ) = curl ( a > 6 > c )> 



.... (23) 



with similar magnetic equations. Since the functions e only 

 differ from unity by amounts of the second order, the equations 

 have, to the first order only, reverted to the original type. 

 The remainder of the argument then follows along the 

 previous lines. 



LXXXVII1. The Indices of Doubly-refracting Crystals, De- 

 termined bij Displacement Inter ferometry . By Carl Barus, 

 Ph.D., LL.D* 

 1. INTRODUCTION. METHOD.— In the following 

 -*■ paper I shall make a further application of the dis- 

 placement interferometer, in endeavouring to investigate a 

 method for the determination of the two refractions of a 

 crystalline plate, with a degree of accuracy approaching the 

 spectrometer and eventually to exceed it. The work is to 

 be extended to all directions of the ordinary and extraordinary 

 ray within the crystal. Inasmuch as the centre of ellipses 



* Communicated by the Author. Abridged from a Report to the 

 Carnegie Institution of Washington, D.C. 



